Remark 1

Let B be a connected unwindable space and let $b$ be a point of B. It follows from Theorem 1, (iv), that every operation of the group $\pi_1(B, b)$ is admissible. Consequently, every $\pi_1(B, b)$-set is isomorphic to a $\pi_1(B, b)$-set $E_b$, where E is a covering of B (III, p. 318, prop. 7). Recall also (III, p. 310, prop. 2) that if E and $E'$ are coverings of B, the mapping $f\mapsto f_b$ induces a bijection of the set of morphisms of B-spaces from E into $E'$ onto the set of morphisms of $\pi_1(B, b)$-sets from $E_b$ into $E'_b$.

In the language of categories, one says that the functor which associates with a covering E of B the fibre $E_b$ is an equivalence of categories from the category of coverings of B into the category of $\pi_1(B, b)$-sets.